Robust Fundamental Theorem for Continuous Processes
Biagini, Sara; Bouchard, Bruno; Kardaras, Constantinos; Nutz, Marcel (2015), Robust Fundamental Theorem for Continuous Processes, Mathematical Finance. 10.1111/mafi.12110
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1410.4962v2
Journal nameMathematical Finance
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Abstract (EN)We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family inline image of possible physical measures. A robust notion inline image of no-arbitrage of the first kind is introduced; it postulates that a nonnegative, nonvanishing claim cannot be superhedged for free by using simple trading strategies. Our first main result is a version of the fundamental theorem of asset pricing: inline image holds if and only if every inline image admits a martingale measure that is equivalent up to a certain lifetime. The second main result provides the existence of optimal superhedging strategies for general contingent claims and a representation of the superhedging price in terms of martingale measures.
Subjects / KeywordsFundamental Theorem of Asset Pricing; Superhedging duality; Arbitrage of the Firs t Kind; Nondominated Model
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